In this exercise, all the prices are excluding Vat unless specified

\displaystyle \\

\displaystyle \textbf{Question 1: } \text{A person purchases an article for Rs. }6200\text{ and sells it}
\displaystyle \text{to a customer for Rs. }8500.\text{ If the Sales Tax (under VAT) is }8\%,
\displaystyle \text{find the VAT paid by the person.}
\displaystyle \text{Answer:}
\displaystyle \text{Cost price of the article}=\text{Rs. }6200
\displaystyle \text{Selling price of the article}=\text{Rs. }8500
\displaystyle \text{Input VAT}=8\%\text{ of Rs. }6200=\frac{8}{100}\times6200=\text{Rs. }496
\displaystyle \text{Output VAT}=8\%\text{ of Rs. }8500=\frac{8}{100}\times8500=\text{Rs. }680
\displaystyle \therefore \text{VAT payable}=\text{Output VAT}-\text{Input VAT}
\displaystyle =680-496=\text{Rs. }184
\\

\displaystyle \textbf{Question 2: } \text{A purchases an article for Rs. }3600\text{ and sells it to B for}
\displaystyle \text{Rs. }4800.\text{ B in turn sells the article to C for Rs. }5500.\text{ If the}
\displaystyle \text{Sales Tax (under VAT) is }10\%,\text{ find the VAT levied on A and B.}
\displaystyle \text{Answer:}
\displaystyle \textbf{For A:}
\displaystyle \text{Input VAT}=10\%\text{ of Rs. }3600=\text{Rs. }360
\displaystyle \text{Output VAT}=10\%\text{ of Rs. }4800=\text{Rs. }480
\displaystyle \therefore \text{VAT payable by A}=480-360=\text{Rs. }120
\displaystyle \textbf{For B:}
\displaystyle \text{Input VAT}=10\%\text{ of Rs. }4800=\text{Rs. }480
\displaystyle \text{Output VAT}=10\%\text{ of Rs. }5500=\text{Rs. }550
\displaystyle \therefore \text{VAT payable by B}=550-480=\text{Rs. }70
\\

\displaystyle \textbf{Question 3: } \text{A manufacturer buys raw material for Rs. }60000\text{ and pays}
\displaystyle 4\%\text{ tax. He sells the finished stock for Rs. }92000\text{ and charges}
\displaystyle 12.5\%\text{ tax. Find the VAT paid by the manufacturer.}
\displaystyle \text{Answer:}
\displaystyle \text{Cost price of the raw material}=\text{Rs. }60000
\displaystyle \text{Input VAT}=4\%\text{ of Rs. }60000=\frac{4}{100}\times60000=\text{Rs. }2400
\displaystyle \text{Selling price of the finished stock}=\text{Rs. }92000
\displaystyle \text{Output VAT}=12.5\%\text{ of Rs. }92000=\frac{12.5}{100}\times92000=\text{Rs. }11500
\displaystyle \therefore \text{VAT payable}=\text{Output VAT}-\text{Input VAT}
\displaystyle =11500-2400=\text{Rs. }9100
\\

\displaystyle \textbf{Question 4: } \text{The cost of an article to a distributor is Rs. }6000.
\displaystyle \text{He sells it to a trader for Rs. }7500\text{ and the trader sells it to a}
\displaystyle \text{customer for Rs. }8000.\text{ If the VAT rate is }12.5\%,\text{ find the VAT}
\displaystyle \text{paid by the: (i) Distributor \qquad (ii) Trader}
\displaystyle \text{Answer:}
\displaystyle \textbf{For the Distributor:}
\displaystyle \text{Input VAT}=12.5\%\text{ of Rs. }6000=\text{Rs. }750
\displaystyle \text{Output VAT}=12.5\%\text{ of Rs. }7500=\text{Rs. }937.50
\displaystyle \therefore \text{VAT payable by the distributor}=937.50-750=\text{Rs. }187.50
\displaystyle \textbf{For the Trader:}
\displaystyle \text{Input VAT}=12.5\%\text{ of Rs. }7500=\text{Rs. }937.50
\displaystyle \text{Output VAT}=12.5\%\text{ of Rs. }8000=\text{Rs. }1000
\displaystyle \therefore \text{VAT payable by the trader}=1000-937.50=\text{Rs. }62.50
\\

\displaystyle \textbf{Question 5: } \text{The printed price of an article is Rs. }2500.\text{ A wholesaler sells}
\displaystyle \text{it to a retailer at a }20\%\text{ discount and charges Sales Tax at the}
\displaystyle \text{rate of }10\%.\text{ The retailer sells it to a customer at the printed}
\displaystyle \text{price and charges Sales Tax at the same rate. Find:}
\displaystyle \text{(i) The amount paid by the retailer to the wholesaler.}
\displaystyle \text{(ii) The VAT paid by the retailer.}
\displaystyle \text{Answer:}
\displaystyle \text{Printed price of the article}=\text{Rs. }2500
\displaystyle \text{Price after }20\%\text{ discount}=\frac{80}{100}\times2500=\text{Rs. }2000
\displaystyle \text{Sales Tax charged by the wholesaler}=10\%\text{ of Rs. }2000=\text{Rs. }200
\displaystyle \therefore \text{Amount paid by the retailer}=2000+200=\text{Rs. }2200
\displaystyle \text{Input VAT}=10\%\text{ of Rs. }2000=\text{Rs. }200
\displaystyle \text{Output VAT}=10\%\text{ of Rs. }2500=\text{Rs. }250
\displaystyle \therefore \text{VAT payable by the retailer}=250-200=\text{Rs. }50
\\

\displaystyle \textbf{Question 6: } \text{A retailer buys an article for Rs. }800\text{ and pays Sales Tax}
\displaystyle \text{at the rate of }8\%.\text{ The retailer sells the same article for Rs. }1000
\displaystyle \text{and charges Sales Tax at the same rate. Find:}
\displaystyle \text{(i) The price paid by the customer.}
\displaystyle \text{(ii) The amount of VAT paid by the retailer.}
\displaystyle \text{Answer:}
\displaystyle \text{Cost price of the article}=\text{Rs. }800
\displaystyle \text{Input VAT}=8\%\text{ of Rs. }800=\frac{8}{100}\times800=\text{Rs. }64
\displaystyle \text{Selling price of the article}=\text{Rs. }1000
\displaystyle \text{Output VAT}=8\%\text{ of Rs. }1000=\frac{8}{100}\times1000=\text{Rs. }80
\displaystyle \therefore \text{Price paid by the customer}=1000+80=\text{Rs. }1080
\displaystyle \therefore \text{VAT payable by the retailer}=80-64=\text{Rs. }16
\\

\displaystyle \textbf{Question 7: } \text{A shopkeeper buys }15\text{ identical articles for Rs. }840\text{ and}
\displaystyle \text{pays Sales Tax at the rate of }8\%.\text{ He sells }6\text{ of these articles}
\displaystyle \text{at Rs. }65\text{ each and charges Sales Tax at the same rate. Calculate}
\displaystyle \text{the VAT paid against the sale of these six articles.}
\displaystyle \text{Answer:}
\displaystyle \text{Cost price of one article}=\frac{840}{15}=\text{Rs. }56
\displaystyle \text{Cost price of }6\text{ articles}=56\times6=\text{Rs. }336
\displaystyle \text{Input VAT}=8\%\text{ of Rs. }336=\frac{8}{100}\times336=\text{Rs. }26.88
\displaystyle \text{Selling price of }6\text{ articles}=65\times6=\text{Rs. }390
\displaystyle \text{Output VAT}=8\%\text{ of Rs. }390=\frac{8}{100}\times390=\text{Rs. }31.20
\displaystyle \therefore \text{VAT payable}=31.20-26.88=\text{Rs. }4.32
\\

\displaystyle \textbf{Question 8: } \text{The marked price of an article is Rs. }900\text{ and the rate of}
\displaystyle \text{Sales Tax is }6\%.\text{ If, on selling the article at its marked price, a}
\displaystyle \text{retailer has to pay VAT = Rs. }4.80,\text{ find the money paid by him}
\displaystyle \text{(including Sales Tax) for purchasing the article.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the purchase price of the article}=\text{Rs. }x
\displaystyle \text{Input VAT}=6\%\text{ of Rs. }x=\frac{6}{100}x
\displaystyle \text{Output VAT}=6\%\text{ of Rs. }900=\frac{6}{100}\times900=\text{Rs. }54
\displaystyle \text{VAT payable}=\text{Output VAT}-\text{Input VAT}
\displaystyle 54-\frac{6}{100}x=4.80
\displaystyle \frac{6}{100}x=49.20
\displaystyle x=\frac{49.20\times100}{6}=\text{Rs. }820
\displaystyle \text{Money paid by the retailer}=820+6\%\text{ of Rs. }820
\displaystyle =820+\frac{6}{100}\times820=\text{Rs. }869.20
\\

\displaystyle \textbf{Question 9: } \text{A manufacturer marks an article at Rs. }5000.\text{ He sells it to}
\displaystyle \text{a wholesaler at a discount of }25\%\text{ on the marked price and the}
\displaystyle \text{wholesaler sells it to a retailer at a discount of }15\%\text{ on its marked}
\displaystyle \text{price. If the retailer sells it without discount and Sales Tax is }8\%
\displaystyle \text{at each stage, calculate the VAT paid by:}\hfill \text{[ICSE 2010]}
\displaystyle \text{(i) The Wholesaler}\qquad\text{(ii) The Retailer}
\displaystyle \text{Answer:}
\displaystyle \text{Marked price of the article}=\text{Rs. }5000
\displaystyle \text{Price paid by the wholesaler}=\frac{75}{100}\times5000=\text{Rs. }3750
\displaystyle \text{Input VAT of wholesaler}=8\%\text{ of Rs. }3750=\text{Rs. }300
\displaystyle \text{Price paid by the retailer}=\frac{85}{100}\times5000=\text{Rs. }4250
\displaystyle \text{Output VAT of wholesaler}=8\%\text{ of Rs. }4250=\text{Rs. }340
\displaystyle \therefore \text{VAT paid by the wholesaler}=340-300=\text{Rs. }40
\displaystyle \text{Input VAT of retailer}=8\%\text{ of Rs. }4250=\text{Rs. }340
\displaystyle \text{Selling price to the customer}=\text{Rs. }5000
\displaystyle \text{Output VAT of retailer}=8\%\text{ of Rs. }5000=\text{Rs. }400
\displaystyle \therefore \text{VAT paid by the retailer}=400-340=\text{Rs. }60
\\

\displaystyle \textbf{Question 10: } \text{A shopkeeper buys an article at a discount of }30\%\text{ and pays}
\displaystyle \text{Sales Tax at the rate of }8\%.\text{ He sells it to a customer at the}
\displaystyle \text{printed price and charges Sales Tax at the same rate. If the printed}
\displaystyle \text{price is Rs. }2500,\text{ find:}
\displaystyle \text{(i) The price paid by the shopkeeper.}
\displaystyle \text{(ii) The price paid by the customer.}
\displaystyle \text{(iii) The VAT paid by the shopkeeper.}
\displaystyle \text{Answer:}
\displaystyle \text{Printed price of the article}=\text{Rs. }2500
\displaystyle \text{Cost price after }30\%\text{ discount}=\frac{70}{100}\times2500=\text{Rs. }1750
\displaystyle \text{Sales Tax paid by the shopkeeper}=8\%\text{ of Rs. }1750=\text{Rs. }140
\displaystyle \therefore \text{Price paid by the shopkeeper}=1750+140=\text{Rs. }1890
\displaystyle \text{Selling price to the customer}=\text{Rs. }2500
\displaystyle \text{Sales Tax paid by the customer}=8\%\text{ of Rs. }2500=\text{Rs. }200
\displaystyle \therefore \text{Price paid by the customer}=2500+200=\text{Rs. }2700
\displaystyle \text{Input VAT}=8\%\text{ of Rs. }1750=\text{Rs. }140
\displaystyle \text{Output VAT}=8\%\text{ of Rs. }2500=\text{Rs. }200
\displaystyle \therefore \text{VAT paid by the shopkeeper}=200-140=\text{Rs. }60
\\

\displaystyle \textbf{Question 11: } \text{A shopkeeper sells an article at its list price of Rs. }3000
\displaystyle \text{and charges Sales Tax at the rate of }12\%.\text{ If the VAT paid by the}
\displaystyle \text{shopkeeper is Rs. }72,\text{ find the price at which he bought the article}
\displaystyle \text{inclusive of Sales Tax.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the cost price of the article for the shopkeeper}=\text{Rs. }x
\displaystyle \text{Input VAT}=12\%\text{ of Rs. }x=\frac{12}{100}x
\displaystyle \text{Selling price of the article}=\text{Rs. }3000
\displaystyle \text{Output VAT}=12\%\text{ of Rs. }3000=\frac{12}{100}\times3000=\text{Rs. }360
\displaystyle \text{VAT payable}=360-\frac{12}{100}x=72
\displaystyle \frac{12}{100}x=288
\displaystyle x=\frac{288\times100}{12}=\text{Rs. }2400
\displaystyle \text{Sales Tax paid by the shopkeeper}=12\%\text{ of Rs. }2400=\text{Rs. }288
\displaystyle \therefore \text{Price paid by the shopkeeper}=2400+288=\text{Rs. }2688
\\

\displaystyle \textbf{Question 12: } \text{A manufacturer marks an article for Rs. }10000.\text{ He sells}
\displaystyle \text{it to a wholesaler at a }40\%\text{ discount. The wholesaler sells it to}
\displaystyle \text{a retailer at a }20\%\text{ discount on the marked price. If the retailer}
\displaystyle \text{sells it to a customer at a }10\%\text{ discount and Sales Tax is }12\%
\displaystyle \text{at each stage, find the VAT paid by:}
\displaystyle \text{(i) The Wholesaler}\qquad\text{(ii) The Retailer}
\displaystyle \text{Answer:}
\displaystyle \text{Marked price of the article}=\text{Rs. }10000
\displaystyle \text{Price paid by the wholesaler}=\frac{60}{100}\times10000=\text{Rs. }6000
\displaystyle \text{Input VAT of wholesaler}=12\%\text{ of Rs. }6000=\text{Rs. }720
\displaystyle \text{Price paid by the retailer}=\frac{80}{100}\times10000=\text{Rs. }8000
\displaystyle \text{Output VAT of wholesaler}=12\%\text{ of Rs. }8000=\text{Rs. }960
\displaystyle \therefore \text{VAT paid by the wholesaler}=960-720=\text{Rs. }240
\displaystyle \text{Input VAT of retailer}=12\%\text{ of Rs. }8000=\text{Rs. }960
\displaystyle \text{Selling price to the customer}=\frac{90}{100}\times10000=\text{Rs. }9000
\displaystyle \text{Output VAT of retailer}=12\%\text{ of Rs. }9000=\text{Rs. }1080
\displaystyle \therefore \text{VAT paid by the retailer}=1080-960=\text{Rs. }120
\\

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